In this article, we will learn the physics behind the simple reaction engine and the mathematics of the Rocket Equation to understand how we reach for space.
In order for us to appreciate the complexities of commercializing space and understanding where the opportunities and challenges of this endeavor arises from, a simple understanding of sending and maneuvering an object into space is required. Rather than providing a lengthy introduction to rocket science, the elements necessary for the understanding of this series will be included in this article.
The Simple Reaction Engine and Rocket Equation
All types of rocket engines are fundamentally reaction engines – an engine that expels mass in order to produce thrust. They act in accordance with Newton’s third law of motion which is commonly paraphrased as: “For every action there is an equal and opposite reaction.” As energy is needed to accelerate stored propellant and losses would occur through heat and thermal radiation, all reaction engines will always lose energy. However, assuming that the engine is 100% efficient, the energy required to accelerate the exhaust equates to:
(where ve is the exhaust velocity and M is the mass of the expended propellant)
Comparing this with the Tsiolkovsky  rocket equation below, it can be seen that even with a 100% engine efficiency, the majority of the energy supplied ends up as the kinetic energy of the exhaust instead of ending up in the vehicle itself.
(where ∆v is the maximum change of velocity of the vehicle given that there are no external forces acting on it, m0 is the wet mass, mf is the dry mass, Isp is the specific impulse and g0 is standard gravity)
For a mission with a fixed delta-v (∆v), there is a particular specific impulse that minimises the rocket’s overall energy use which comes to an exhaust velocity of about . In what NASA’s Flight Engineer Don Pettit  has coined “the tyranny of the rocket equation”, there is a certain limit in the amount of payload a rocket can carry, as more propellant increases the overall weight, thus requiring greater fuel consumption. This is one of the contributing factors that makes launching payloads into space such an expensive enterprise.
Building upon the concept of reaction engines, the majority of rocket engines combusts reactive chemicals to supply the energy necessary to propel high-temperature gas at high-speeds in order to produce thrust. For the sake of simplicity, all current launch vehicles can be classified into three types that share the same operating principle: the liquid-fuel, solid-fuel and bi-propellant rocket (readers might want to take note that there are other forms of propulsion that will be covered in a later article).
As seen in Figure 1, liquid-fueled rockets store fuel (1) and oxidizer (2) components in separate compartments. Pumps (3) are used to force them into a combustion chamber (4) where they mix and burn. The subsequent hot exhaust is choked at the nozzle (5) where it is dramatically accelerated into a supersonic jet that exits the rocket (6) and propels it in the opposite direction.
Contrasting the liquid-fueled rocket, Figure 2 shows the propellant – a prepared mixture of oxidizing components and fuel called ‘grain’ (1) of a solid-fuel rocket forming a combustion chamber (3) via a cylindrical hole in its storage casing. An igniter (2) combusts the surface of the propellant and the hot exhaust is channeled into the nozzle (4) where it then undergoes the same acceleration seen in a liquid-fuel rocket and expelled (5).
The knowledge of the principle operation of these two rocket engines is sufficient enough for us to understand the bi-propellant rocket engine without a lengthy explanation. There are many sub-classes of bi-propellant rocket engines that incorporates different power cycles which affects the performance of the engine. As it is not necessary for the understanding of this series, curious readers can refer to Sutton’s ‘Rocket Propulsion Elements’ and ‘History of Liquid Propellant Rocket Engines’ instead for further information .
End of Part II
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 Tsiolkovsky, K. E. (2004). Selected Works of Konstantin E. Tsiolkovsky. Blagonravov, A. A., University Press of the Pacific.
 Sutton, G. P. & Biblarz, O. (2000). Rocket propulsion elements. 7th ed., John Wiley & Sons.
 Pettit, D. (2012). The Tyranny of the Rocket Equation, NASA.
 Wikipedia Contributors (2018). Liquid-Fuel Rocket Diagram, Wikipedia Commons.
 Wikipedia Contributors (2018). Solid-Fuel Rocket Diagram, Wikipedia Commons.
 Sutton, G. P. (2005) History of Liquid Propellant Rocket Engines. American Institute of Aeronautics and Astronautics.